Nonparametric Methods for Modeling Nonlinearity in Regression Analysis
Bibliographic record
Abstract
The linear model and related generalized linear model (GLM) are important tools for sociologists. If the relationships between y (or in the case of the GLM, the linear predictor η) and the xs are linear, these methods provide elegant summaries of the data. However, these methods fail to adequately model underlying relationships if they are characterized by complex nonlinear patterns. In such cases, nonparametric regression, which allows the functional form between y and x to be determined by the data themselves, is more suitable. There are many types of nonparametric simple regression. I focus on locally weighted scatterplot smoothing (lowess or loess) and smoothing splines because they are the most widely used. I also describe additive and generalized additive models (GAM), which allow modeling of categorical dependent variables, and I explain how these methods can handle both parametric and nonparametric (i.e., lowess and smoothing splines) effects for many predictors. Finally, I briefly introduce the more recent development of the vector generalized additive model (VGAM), which further extends the GAM to handle multivariate dependent variables, and the generalized additive mixed model (GAMM), which allows specification of smooth functions within the mixed model framework.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.024 | 0.098 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.003 |
| Bibliometrics | 0.004 | 0.006 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.003 | 0.004 |
| Open science | 0.004 | 0.004 |
| Research integrity | 0.003 | 0.006 |
| Insufficient payload (model declined to judge) | 0.008 | 0.003 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".